This is a renewal application for a grant currently entitled "Computer Technology for Transaxial Tomography". The change in title to "Reconstruction and Display in Tomographic Radiology" reflects a shift in the nature of the proposed work. We propose to cover various modalities in radiology--namely, computerized tomography (CT), positron emission tomography (PET), magnetic resonance imaging (MRI) and ultrasound (US)--all of which are tomographic in the sense that they produce images of slices through the human body. "Reconstruction" in the title of the proposal is to be interpreted as the procedure to produce such images from the measured raw data in CT, PET, and MRI. "Display" in the title is to be interpreted as the procedure to put together in three-dimensional (3D)--or (including time) 4D--space the information that exists in the individual slices. In "reconstruction" we plan to concentrate on finite series expansion methods, methods derived from a semi-continuous formulation, preprocessing of incomplete or distorted data, with applications to CT, PET, and MRI. In "display" we plan to concentrate on segmentation (identification of structures of interest, such as specific organs and tumors, in the 3D space) and on rapid display, analysis, and manipulation of the identified structures, with applications to measurement of volumetric changes in soft-tissue masses, surgical planning, radiation therapy treatment planning, and characterization of the normal, ischemic and scarred myocardium. In all cases computer software will be fully developed, implemented, tested, and evaluated, on the kind of computing equipment that is commonly available in radiology departments.